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Uniform estimate of dimension of the global attractor for a semi-discretized chemotaxis-growth system

Pages: 334 - 343, Issue Special, September 2007

 Abstract        Full Text (231.1K)              

Messoud Efendiev - Department of Mathematics, Technical University of Muinch, Boltzmannstrasse 3, 85747 Garching, Germany (email)
Etsushi Nakaguchi - Graduate School of Information Science and Technology, Osaka University, 2-1 Yamadaoka, Suita, Osaka 565-0871, Japan (email)
Wolfgang L. Wendland - Department of Mathematics, University of Stuttgart, Pfaffenwaldring 57, 70550 Stuttgart, Germany (email)

Abstract: We study a finite-element approximation of the chemotaxis-growth system. We establish dimension estimate of global attractors for the approximate systems. Our results show that the estimates are uniform with respect to the discretization parameter and polynomial order with respect to the chemotactic coefficient in the equation.We especially emphasize that, this is just the same order (polynomial) as for the original system obtained in the preceding papers [Adv.Math.Sci.Appl. Part I and II].

Keywords:  Dimension of global attractor, finite-element approximation, chemotaxis-growth system.
Mathematics Subject Classification:  Primary: 37L30, 65M60; Secondary: 35K57, 92C15.

Received: August 2006;      Revised: January 2007;      Published: September 2007.